{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T20:22:26Z","timestamp":1768076546846,"version":"3.49.0"},"reference-count":57,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T00:00:00Z","timestamp":1614902400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T00:00:00Z","timestamp":1614902400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s10208-021-09497-w","type":"journal-article","created":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T22:02:30Z","timestamp":1614981750000},"page":"1703-1737","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Newton Polytopes and Relative Entropy Optimization"],"prefix":"10.1007","volume":"21","author":[{"given":"Riley","family":"Murray","sequence":"first","affiliation":[]},{"given":"Venkat","family":"Chandrasekaran","sequence":"additional","affiliation":[]},{"given":"Adam","family":"Wierman","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,5]]},"reference":[{"issue":"1","key":"9497_CR1","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1080\/23307706.2017.1397554","volume":"5","author":"A Agrawal","year":"2018","unstructured":"Agrawal, A., Verschueren, R., Diamond, S., Boyd, S.: A rewriting system for convex optimization problems. Journal of Control and Decision 5(1), 42\u201360 (2018)","journal-title":"Journal of Control and Decision"},{"key":"9497_CR2","doi-asserted-by":"crossref","unstructured":"Ahmadi, A., Majumdar, A.: DSOS and SDSOS optimization: LP and SOCP-based alternatives to sum of squares optimization. In: 2014 48th Annual Conference on Information Sciences and Systems (CISS), pp. 1\u20135 (2014)","DOI":"10.1109\/CISS.2014.6814141"},{"key":"9497_CR3","doi-asserted-by":"publisher","unstructured":"August, E., Craciun, G., Koeppl, H.: Finding invariant sets for biological systems using monomial domination. In: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC). IEEE (2012). https:\/\/doi.org\/10.1109\/cdc.2012.6426491","DOI":"10.1109\/cdc.2012.6426491"},{"issue":"3","key":"9497_CR4","doi-asserted-by":"publisher","first-page":"1542","DOI":"10.1137\/140980624","volume":"25","author":"T Bajbar","year":"2015","unstructured":"Bajbar, T., Stein, O.: Coercive polynomials and their newton polytopes. SIAM Journal on Optimization 25(3), 1542\u20131570 (2015)","journal-title":"SIAM Journal on Optimization"},{"issue":"11","key":"9497_CR5","doi-asserted-by":"publisher","first-page":"1581","DOI":"10.1016\/S0098-1354(02)00129-1","volume":"26","author":"KM Bj\u00f6rk","year":"2002","unstructured":"Bj\u00f6rk, K.M., Westerlund, T.: Global optimization of heat exchanger network synthesis problems with and without the isothermal mixing assumption. Computers & Chemical Engineering 26(11), 1581\u20131593 (2002)","journal-title":"Computers & Chemical Engineering"},{"issue":"1","key":"9497_CR6","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/s11081-007-9001-7","volume":"8","author":"S Boyd","year":"2007","unstructured":"Boyd, S., Kim, S.J., Vandenberghe, L., Hassibi, A.: A tutorial on geometric programming. Optimization and Engineering 8(1), 67\u2013127 (2007)","journal-title":"Optimization and Engineering"},{"issue":"2","key":"9497_CR7","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.1137\/140988978","volume":"26","author":"V Chandrasekaran","year":"2016","unstructured":"Chandrasekaran, V., Shah, P.: Relative entropy relaxations for signomial optimization. SIAM Journal on Optimization 26(2), 1147 \u2013 1173 (2016)","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"9497_CR8","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1007\/BF01608996","volume":"15","author":"R Dembo","year":"1978","unstructured":"Dembo, R., Avriel, M.: Optimal design of a membrane separation process using signomial programming. Mathematical Programming 15(1), 12\u201325 (1978)","journal-title":"Mathematical Programming"},{"issue":"83","key":"9497_CR9","first-page":"1","volume":"17","author":"S Diamond","year":"2016","unstructured":"Diamond, S., Boyd, S.: CVXPY: A Python-embedded modeling language for convex optimization. Journal of Machine Learning Research 17(83), 1\u20135 (2016)","journal-title":"Journal of Machine Learning Research"},{"key":"9497_CR10","doi-asserted-by":"crossref","unstructured":"Domahidi, A., Chu, E., Boyd, S.: ECOS: An SOCP solver for embedded systems. In: European Control Conference (ECC), pp. 3071\u20133076 (2013)","DOI":"10.23919\/ECC.2013.6669541"},{"issue":"1","key":"9497_CR11","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1137\/16M1086303","volume":"1","author":"M Dressler","year":"2017","unstructured":"Dressler, M., Iliman, S., de\u00a0Wolff, T.: A positivstellensatz for sums of nonnegative circuit polynomials. SIAM Journal on Applied Algebra and Geometry 1(1), 536\u2013555 (2017)","journal-title":"SIAM Journal on Applied Algebra and Geometry"},{"key":"9497_CR12","unstructured":"Forsg\u00e5rd, J., de\u00a0Wolff, T.: The lattice of amoebas (2017)"},{"issue":"2","key":"9497_CR13","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/s10589-013-9596-x","volume":"57","author":"M Ghasemi","year":"2013","unstructured":"Ghasemi, M., Lasserre, J.B., Marshall, M.: Lower bounds on the global minimum of a polynomial. Computational Optimization and Applications 57(2), 387\u2013402 (2013)","journal-title":"Computational Optimization and Applications"},{"issue":"2","key":"9497_CR14","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1137\/110836869","volume":"22","author":"M Ghasemi","year":"2012","unstructured":"Ghasemi, M., Marshall, M.: Lower bounds for polynomials using geometric programming. SIAM Journal on Optimization 22(2), 460\u2013473 (2012)","journal-title":"SIAM Journal on Optimization"},{"key":"9497_CR15","doi-asserted-by":"publisher","unstructured":"Hall, D., Dowdle, A., Gonzalez, J., Trollinger, L., Thalheimer, W.: Assessment of a boundary layer ingesting turboelectric aircraft configuration using signomial programming. In: 2018 Aviation Technology, Integration, and Operations Conference. American Institute of Aeronautics and Astronautics (2018). https:\/\/doi.org\/10.2514\/6.2018-3973","DOI":"10.2514\/6.2018-3973"},{"issue":"3","key":"9497_CR16","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1007\/BF01443605","volume":"32","author":"D Hilbert","year":"1888","unstructured":"Hilbert, D.: Ueber die darstellung definiter formen als summe von formenquadraten. Mathematische Annalen 32(3), 342\u2013350 (1888)","journal-title":"Mathematische Annalen"},{"issue":"1","key":"9497_CR17","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1186\/s40687-016-0052-2","volume":"3","author":"S Iliman","year":"2016","unstructured":"Iliman, S., de\u00a0Wolff, T.: Amoebas, nonnegative polynomials and sums of squares supported on circuits. Research in the Mathematical Sciences 3(1), 9 (2016). https:\/\/doi.org\/10.1186\/s40687-016-0052-2","journal-title":"Research in the Mathematical Sciences"},{"issue":"2","key":"9497_CR18","doi-asserted-by":"publisher","first-page":"1128","DOI":"10.1137\/140962425","volume":"26","author":"S Iliman","year":"2016","unstructured":"Iliman, S., de\u00a0Wolff, T.: Lower bounds for polynomials with simplex newton polytopes based on geometric programming. SIAM Journal on Optimization 26(2), 1128\u20131146 (2016)","journal-title":"SIAM Journal on Optimization"},{"issue":"2","key":"9497_CR19","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1108\/03321640710727809","volume":"26","author":"R Jabr","year":"2007","unstructured":"Jabr, R.: Inductor design using signomial programming. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 26(2), 461\u2013475 (2007)","journal-title":"COMPEL - The international journal for computation and mathematics in electrical and electronic engineering"},{"key":"9497_CR20","doi-asserted-by":"crossref","unstructured":"Karaca, O., Darivianakis, G., Beuchat, P., Georghiou, A., Lygeros, J.: The REPOP toolbox: Tackling polynomial optimization using relative entropy relaxations. IFAC-PapersOnLine 50(1), 11652 \u2013 11657 (2017). 20th IFAC World Congress","DOI":"10.1016\/j.ifacol.2017.08.1669"},{"key":"9497_CR21","unstructured":"Khovanskii, A.: Fewnomials and pfaff manifolds. In: Proceedings of the International Congress of Mathematicians, vol.\u00a01 (1983)"},{"key":"9497_CR22","doi-asserted-by":"crossref","unstructured":"Khovanskii, A.: Fewnomials, vol.\u00a088. American Mathematical Soc. (1991)","DOI":"10.1090\/mmono\/088"},{"issue":"3","key":"9497_CR23","doi-asserted-by":"publisher","first-page":"965","DOI":"10.2514\/1.C034378","volume":"55","author":"P Kirschen","year":"2018","unstructured":"Kirschen, P., York, M., Ozturk, B., Hoburg, W.: Application of signomial programming to aircraft design. Journal of Aircraft 55(3), 965\u2013987 (2018)","journal-title":"Journal of Aircraft"},{"issue":"1","key":"9497_CR24","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/s10107-004-0554-3","volume":"103","author":"M Kojima","year":"2004","unstructured":"Kojima, M., Kim, S., Waki, H.: Sparsity in sums of squares of polynomials. Mathematical Programming 103(1), 45\u201362 (2004)","journal-title":"Mathematical Programming"},{"key":"9497_CR25","doi-asserted-by":"crossref","unstructured":"Krivine, J.L.: Anneaux pr\u00e9ordonn\u00e9s. Journal d\u2019analyse math\u00e9matique 12, p. 307\u2013326 (1964)","DOI":"10.1007\/BF02807438"},{"key":"9497_CR26","doi-asserted-by":"crossref","unstructured":"Kwan, H., Ho, Y., Wong, N., Ho, K.: Designing globally optimal delta-sigma modulator topologies via signomial programming. In: 2007 International Symposium on VLSI Design, Automation and Test (VLSI-DAT), pp. 1\u20134 (2007)","DOI":"10.1109\/VDAT.2007.373209"},{"issue":"3","key":"9497_CR27","doi-asserted-by":"publisher","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"JB Lasserre","year":"2001","unstructured":"Lasserre, J.B.: Global optimization with polynomials and the problem of moments. SIAM Journal on Optimization 11(3), 796\u2013817 (2001)","journal-title":"SIAM Journal on Optimization"},{"issue":"4","key":"9497_CR28","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1016\/S0098-1354(96)00282-7","volume":"21","author":"C Maranas","year":"1997","unstructured":"Maranas, C., Floudas, C.: Global optimization in generalized geometric programming. Computers & Chemical Engineering 21(4), 351\u2013369 (1997)","journal-title":"Computers & Chemical Engineering"},{"key":"9497_CR29","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/146","author":"M Marshall","year":"2008","unstructured":"Marshall, M.: Positive Polynomials and Sums of Squares. American Mathematical Society (2008). https:\/\/doi.org\/10.1090\/surv\/146","journal-title":"American Mathematical Society"},{"issue":"1","key":"9497_CR30","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s10208-014-9239-3","volume":"16","author":"S M\u00fcller","year":"2015","unstructured":"M\u00fcller, S., Feliu, E., Regensburger, G., Conradi, C., Shiu, A., Dickenstein, A.: Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry. Foundations of Computational Mathematics 16(1), 69\u201397 (2015)","journal-title":"Foundations of Computational Mathematics"},{"key":"9497_CR31","doi-asserted-by":"crossref","unstructured":"M\u00fcller, S., Hofbauer, J., Regensburger, G.: On the bijectivity of families of exponential\/generalized polynomial maps (2018)","DOI":"10.1137\/18M1178153"},{"issue":"2","key":"9497_CR32","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/BF02592948","volume":"39","author":"K Murty","year":"1987","unstructured":"Murty, K., Kabadi, S.: Some NP-complete problems in quadratic and nonlinear programming. Mathematical Programming 39(2), 117\u2013129 (1987)","journal-title":"Mathematical Programming"},{"key":"9497_CR33","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970791","volume-title":"Interior-point polynomial algorithms in convex programming","author":"Y Nesterov","year":"1994","unstructured":"Nesterov, Y., Nemirovskii, A.: Interior-point polynomial algorithms in convex programming. Society for Industrial and Applied Mathematics, Philadelphia (1994)"},{"issue":"4","key":"9497_CR34","doi-asserted-by":"publisher","first-page":"1534","DOI":"10.1137\/060668791","volume":"19","author":"J Nie","year":"2009","unstructured":"Nie, J., Demmel, J.: Sparse SOS relaxations for minimizing functions that are summations of small polynomials. SIAM Journal on Optimization 19(4), 1534\u20131558 (2009)","journal-title":"SIAM Journal on Optimization"},{"key":"9497_CR35","unstructured":"Opgenoord, M., Cohen, B., Hoburg, W.: Comparison of algorithms for including equality constraints in signomial programming. Tech. Rep. ACDL TR-2017-1, MIT (2017)"},{"key":"9497_CR36","unstructured":"Oxley, J.: What is a matroid? https:\/\/www.math.lsu.edu\/~oxley\/survey4.pdf (2014)"},{"issue":"6","key":"9497_CR37","doi-asserted-by":"publisher","first-page":"2153","DOI":"10.3934\/dcdsb.2012.17.2153","volume":"17","author":"C Pantea","year":"2012","unstructured":"Pantea, C., Koeppl, H., Craciun, G.: Global injectivity and multiple equilibria in uni- and bi-molecular reaction networks. Discrete and Continuous Dynamical Systems - Series B 17(6), 2153\u20132170 (2012)","journal-title":"Discrete and Continuous Dynamical Systems - Series B"},{"key":"9497_CR38","unstructured":"Papp, D., Y1l1z, S.: On \u201ca homogeneous interior-point algorithm for non-symmetric convex conic optimization\u201d (2017)"},{"key":"9497_CR39","unstructured":"Parillo, P.: Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. Ph.D. thesis, California Institute of Technology, Pasadena, CA (2000)"},{"key":"9497_CR40","doi-asserted-by":"publisher","unstructured":"P\u00e9bay, P., Rojas, J.M., Thompson, D.: Optimization and NP\\_r-completeness of certain fewnomials. In: Proceedings of the 2009 conference on Symbolic numeric computation. ACM Press (2009). https:\/\/doi.org\/10.1145\/1577190.1577212","DOI":"10.1145\/1577190.1577212"},{"issue":"2","key":"9497_CR41","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1215\/S0012-7094-78-04519-2","volume":"45","author":"B Reznick","year":"1978","unstructured":"Reznick, B.: Extremal PSD forms with few terms. Duke Mathematical Journal 45(2), 363\u2013374 (1978)","journal-title":"Duke Mathematical Journal"},{"issue":"3","key":"9497_CR42","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1007\/BF01442738","volume":"283","author":"B Reznick","year":"1989","unstructured":"Reznick, B.: Forms derived from the arithmetic-geometric inequality. Mathematische Annalen 283(3), 431\u2013464 (1989)","journal-title":"Mathematische Annalen"},{"issue":"2","key":"9497_CR43","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/BF00934080","volume":"38","author":"D Rountree","year":"1982","unstructured":"Rountree, D., Rigler, A.: A penalty treatment of equality constraints in generalized geometric programming. Journal of Optimization Theory and Applications 38(2), 169\u2013178 (1982)","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"3","key":"9497_CR44","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/S0022-4049(01)00041-X","volume":"166","author":"M Schweighofer","year":"2002","unstructured":"Schweighofer, M.: An algorithmic approach to Schm\u00fcdgen\u2019s Positivstellensatz. Journal of Pure and Applied Algebra 166(3), 307\u2013319 (2002)","journal-title":"Journal of Pure and Applied Algebra"},{"key":"9497_CR45","unstructured":"Seidler, H., de\u00a0Wolff, T.: An experimental comparison of SONC and SOS certificates for unconstrained optimization (2018)"},{"key":"9497_CR46","unstructured":"Seidler, H., de\u00a0Wolff, T.: POEM: Effective methods in polynomial optimization, version 0.2.1.0(a). http:\/\/www.iaa.tu-bs.de\/AppliedAlgebra\/POEM\/index.html (2019)"},{"key":"9497_CR47","unstructured":"Serrano, S.: Algorithms for unsymmetric cone optimization and an implementation for problems with the exponential cone. Ph.D. thesis, Stanford University, Palo Alto, CA (2015)"},{"issue":"1","key":"9497_CR48","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1016\/j.amc.2003.12.101","volume":"162","author":"P Shen","year":"2005","unstructured":"Shen, P.: Linearization method of global optimization for generalized geometric programming. Applied Mathematics and Computation 162(1), 353\u2013370 (2005)","journal-title":"Applied Mathematics and Computation"},{"issue":"3","key":"9497_CR49","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1023\/A:1008249414776","volume":"12","author":"H Sherali","year":"1998","unstructured":"Sherali, H.: Global optimization of nonconvex polynomial programming problems having rational exponents. Journal of Global Optimization 12(3), 267\u2013283 (1998)","journal-title":"Journal of Global Optimization"},{"issue":"6","key":"9497_CR50","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1007\/BF01070233","volume":"23","author":"NZ Shor","year":"1988","unstructured":"Shor, N.Z.: Class of global minimum bounds of polynomial functions. Cybernetics 23(6), 731\u2013734 (1988)","journal-title":"Cybernetics"},{"issue":"8\u20139","key":"9497_CR51","doi-asserted-by":"publisher","first-page":"1117","DOI":"10.1002\/mana.201000130","volume":"285","author":"J Silipo","year":"2012","unstructured":"Silipo, J.: The Ronkin number of an exponential sum. Mathematische Nachrichten 285(8-9), 1117\u20131129 (2012)","journal-title":"Mathematische Nachrichten"},{"issue":"2","key":"9497_CR52","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s10107-014-0773-1","volume":"150","author":"A Skajaa","year":"2014","unstructured":"Skajaa, A., Ye, Y.: A homogeneous interior-point algorithm for nonsymmetric convex conic optimization. Mathematical Programming 150(2), 391\u2013422 (2014)","journal-title":"Mathematical Programming"},{"issue":"3","key":"9497_CR53","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/s002080010009","volume":"1","author":"L Tun\u00e7el","year":"2001","unstructured":"Tun\u00e7el, L.: Generalization of primal\u2014dual interior-point methods to convex optimization problems in conic form. Foundations of Computational Mathematics 1(3), 229\u2013254 (2001)","journal-title":"Foundations of Computational Mathematics"},{"issue":"1","key":"9497_CR54","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1137\/050623802","volume":"17","author":"H Waki","year":"2006","unstructured":"Waki, H., Kim, S., Kojima, M., Muramatsu, M.: Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity. SIAM Journal on Optimization 17(1), 218\u2013242 (2006)","journal-title":"SIAM Journal on Optimization"},{"key":"9497_CR55","unstructured":"Wang, J.: Nonnegative polynomials and circuit polynomials. arXiv:1804.09455v1 (2018)"},{"key":"9497_CR56","unstructured":"Wang, J.: On supports of sums of nonnegative circuit polynomials. arXiv:1809.10608v1 (2018)"},{"key":"9497_CR57","doi-asserted-by":"crossref","unstructured":"Yan, J.: Signomial programs with equality constraints: numerical solution and applications. Ph.D. thesis, University of British Columbia (1976)","DOI":"10.6010\/geoinformatics1975.1976.2_66"}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09497-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10208-021-09497-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-021-09497-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T17:05:57Z","timestamp":1637600757000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10208-021-09497-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,5]]},"references-count":57,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["9497"],"URL":"https:\/\/doi.org\/10.1007\/s10208-021-09497-w","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,5]]},"assertion":[{"value":"8 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 May 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 December 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}